Effect of Step Stiffness and Diffusion Anisotropy on the Meandering of a Growing Vicinal Surface

Abstract

We study the step meandering instability on a surface characterized by the alternation of terraces with different properties, as in the case of Si(001). The interplay between diffusion anisotropy and step stiffness induces a finite wavelength instability corresponding to a meandering mode. The instability sets in beyond a threshold value which depends on the relative magnitudes of the destabilizing flux and the stabilizing stiffness difference. The meander dynamics is governed by the conserved Kuramoto-Sivashinsky equation, which display spatiotemporal coarsening.

Universal non-equilibrium phenomena at submicrometric surfaces and interfaces

“…Second, due to the Ehrlich-Schwoebel effect the kinetic coefficients k (±) D for adatom attachment from the different sides of a step may now differ, which is the physical origin for the morphological (known as meandering) instability, first elucidated by Bales and Zangwill [59]. Within a quasistationary approximation in which concentration at terraces is taken to relax faster than any other process and assuming a weak ES effect, it has recently been shown [58] that the effective interface equation for an isolated step has the following form in non-dimensional units:…”

“…Following the seminal work of Burton, Cabrera and Frank [2,9], a MB problem can be formulated in which diffusion of adatoms takes place on terraces, step motion being due to the resulting diffusive fluxes at the step. In the absence of adatom evaporation on terraces and for a constant driving adatom flux F on the terraces, one has the following MB problem [58]:…”

Observation and Modeling of Interrupted Pattern Coarsening: Surface Nanostructuring by Ion Erosion

“…The former is the celebrated Kuramoto-Sivashinsky (KS) equation [27,28], paradigmatic of spatiotemporal chaos, for which a (disordered) short-range pattern develops with a wavelength that does not coarsen, kinetic roughening occuring at much larger scales [29]. The 1 ¼ 0 case is the ''conserved'' KS equation (CKS), appearing, for dynamics of amorphous thin films [13] and steps on vicinal surfaces [30], for which the linear instability leads to an ordered pattern of paraboloids with uninterrupted coarsening.…”

From the conserved Kuramoto–Sivashinsky equation to a coalescing particles model

“…Recently, T. Frisch and A. Verga have found [15,16] that in special limits 1 the profile u(x, t) of the wandering steps satisfies the equation…”

“…The propagative term can be removed using the transformation u → u + (γ/2)x, which, however, introduces γ−dependent boundary conditions [17]. Numerics and heuristic/similarity arguments give a coarsening pattern whose typical length scale grows asl ∼ t n , with a coarsening exponent n = 1 2 , both in the presence [17,18] and in the absence [15] of the propagative term.…”